scholarly journals Nominal Logic with Equations Only

2011 ◽  
Vol 71 ◽  
pp. 44-57
Author(s):  
Ranald Clouston
Keyword(s):  
Nominal Logic

scholarly journals Formalising the pi-calculus using nominal logic

2009 ◽  
Vol 5 (2) ◽  
Author(s):  
Jesper Bengtson ◽  
Joachim Parrow
Keyword(s):  
Pi Calculus ◽  
Nominal Logic

scholarly journals αCheck: A mechanized metatheory model checker

2017 ◽  
Vol 17 (3) ◽  
pp. 311-352 ◽  
Author(s):  
JAMES CHENEY ◽  
ALBERTO MOMIGLIANO
Keyword(s):  
Programming Language ◽  
Dual Problem ◽  
State Of The Art ◽  
Operational Semantics ◽  
Type Systems ◽  
Model Checker ◽  
Formal Systems ◽  
Current State ◽  
Fully Automatic ◽  
Nominal Logic

AbstractThe problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual problem of searching for errors in such formalizations has attracted comparatively little attention. In this article, we present αCheck, a bounded model checker for metatheoretic properties of formal systems specified using nominal logic. In contrast to the current state of the art for metatheory verification, our approach is fully automatic, does not require expertise in theorem proving on the part of the user, and produces counterexamples in the case that a flaw is detected. We present two implementations of this technique, one based onnegation-as-failureand one based onnegation elimination, along with experimental results showing that these techniques are fast enough to be used interactively to debug systems as they are developed.

scholarly journals A simple sequent calculus for nominal logic

2014 ◽  
Vol 26 (2) ◽  
pp. 699-726 ◽  
Author(s):  
James Cheney
Keyword(s):  
Sequent Calculus ◽  
Nominal Logic

Permissive-nominal logic

2012 ◽  
Vol 13 (3) ◽  
pp. 1-36 ◽  
Author(s):  
Gilles Dowek ◽  
Murdoch J. Gabbay
Keyword(s):  
Nominal Logic

scholarly journals Nominal logic programming

2008 ◽  
Vol 30 (5) ◽  
pp. 1-47 ◽  
Author(s):  
James Cheney ◽  
Christian Urban
Keyword(s):  
Logic Programming ◽  
Nominal Logic

Completeness and Herbrand theorems for nominal logic

2006 ◽  
Vol 71 (1) ◽  
pp. 299-320 ◽  
Author(s):  
James Cheney
Keyword(s):  
Set Theory ◽  
Order Logic ◽  
Theory And Practice ◽  
First Order Logic ◽  
Abstract Syntax ◽  
Finite Support ◽  
First Order ◽  
Nominal Logic ◽  
Abstract Syntax Trees ◽  
Herbrand Models

AbstractNominal logic is a variant of first-order logic in which abstract syntax with names and binding is formalized in terms of two basic operations: name-swapping andfreshness. It relies on two important principles: equivariance (validity is preserved by name-swapping), and fresh name generation (“new” or fresh names can always be chosen). It is inspired by a particular class of models for abstract syntax trees involving names and binding, drawing on ideas from Fraenkel-Mostowski set theory: finite-support models in which each value can depend on only finitely many names.Although nominal logic is sound with respect to such models, it is not complete. In this paper we review nominal logic and show why finite-support models are insufficient both in theory and practice. We then identify (up to isomorphism) the class of models with respect to which nominal logic is complete: ideal-supported models in which the supports of values are elements of a proper ideal on the set of names.We also investigate an appropriate generalization of Herbrand models to nominal logic. After adjusting the syntax of nominal logic to include constants denoting names, we generalize universal theories to nominal-universal theories and prove that each such theory has an Herbrand model.

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